Infinite Order Hydrodynamics: An Analytical Example

Abstract

We construct a kinetic model for matter-radiation interactions whose hydrodynamic gradient expansion can be computed analytically up to infinite order in derivatives, in the fully nonlinear regime, and for arbitrary flows. The frequency dependence of the opacity of matter is chosen to mimic the relaxation time of a self-interacting scalar field. In this way, the transient sector simulates that of a realistic quantum field theory. The gradient series is found to diverge for most flows, in agreement with previous findings. We identify, for the model at hand, the mechanism at the origin of the divergence, and we provide a successful regularization scheme. Additionally, we propose a universal qualitative framework for predicting the breakdown of the gradient expansion of an arbitrary microscopic system undergoing a given flow. This framework correctly recovers all previously known instances of gradient expansion divergence. As a new prediction, we show that the gradient expansion diverges when the energy-dependent mean free path is unbounded above.

7 pages (main text) + 2 pages (supplemetary material), 2 captioned figures. Published on PRL (see https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.032302)

References in corpus (15)

• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Truncated Moment Formalism for Radiation Hydrodynamics in Numerical Relativity
• Semi-implicit scheme for treating radiation under M1 closure in general relativistic conservative fluid dynamics codes
• The stickiness of sound: An absolute lower limit on viscosity and the breakdown of second order relativistic hydrodynamics
• Anisotropic Hydrodynamics: Three lectures
• Origin of the Relaxation Time in Dissipative Fluid Dynamics
• On the convergence of the gradient expansion in hydrodynamics
• Relativistic Radiation Magnetohydrodynamics in Dynamical Spacetimes: Numerical Methods and Tests
• Relativistic Hydrodynamic Attractors with Broken Symmetries: Non-Conformal and Non-Homogeneous
• Theories of Relativistic Dissipative Fluid Dynamics
• Bounds on transport from hydrodynamic stability
• Dispersion relations alone cannot guarantee causality
• The regime of applicability of Israel-Stewart hydrodynamics
• Far-from-equilibrium kinetic dynamics of $\lambda {\varphi }^4$ theory in an expanding universe
• Relativistic heat conduction in the large-flux regime

Cited by in corpus (6)

• Gapless non-hydrodynamic modes in relativistic kinetic theory
• Branch-cut in the shear-stress response function of massless $\lambda {\phi }^4$ with Boltzmann statistics
• Convergence of the hydrodynamic gradient expansion in relativistic kinetic theory
• Field redefinition and its impact in relativistic hydrodynamics
• Heat propagation in rotating relativistic bodies
• Thermoelectric Conduction in General Relativity: A Causal, Stable, and Well Posed Theory